Advancements in magnetic memory may ultimately achieve areal densities that exceed 5 Tb/inch. Such areal densities will likely require bit aspect ratios (BAR, which equals track width/bit length) from 2 to 1. In order for a reader to achieve the required down-track and cross-track resolution necessary to read from such memory, shielding from all sides will likely be required. At the noted BAR, the magnetic sensor and magnetic biasing elements would need to fit within extremely small areas (a square of 272 nm2 or a rectangle of 253 nm2). Magnetic sensors as currently designed, will be extremely difficult or impossible to scale down to this size. Therefore, there remains a need for novel magnetic sensor designs that can be scaled down to this level.